Some small-business owners are coming to grips with the reality that Amazon.com Inc. is not just a partner—it is a rival, too.

Among them is Jordan Lindberg of Traverse City, Mich., whose four-year-old business, Stardust Memorials LLC, sells cremation urns. So far, about 10% of his firm’s $3 million annual sales is from Amazon buyers. He pays Amazon a 15% fee on every sale through the site. “If you say no to Amazon, you’re closing the door on tons of sales,” he said.